do you have much competition
In Australia, absolutely. Regardless of whether it's a big studio or just a couple dudes in a basement, it seems like every games company on this side of the pond only wants the most experienced programmers. It's a problem with indie development; they simply can't afford to take on trainees, yet the trainees can't find any places to build experience and their resume.
I also find that most people who are interested in doing games down here are really intensely focused on the code-side, rather than the art. With less studios, less positions and more potential candidates, you have to work harder to prove yourself. I also hear that studios don't take on candidates who have never worked in a professional studio before.
are there freelance programmers
Of course; most of the people at 2and2 (where I'm now going to be working) are contractors who will do a project or two and then take off. It's more of an indie thing, however; indies like contractors because they're cheaper and they're more likely to just do the work without bitching about it, whereas the bigger studios want to stick with internal staff who will meet their specific requirements.
do you get to stay even after a game is done
If you're a contractor, that's up to what you sign on. If you're an actual employee; programming is a MUCH more stable position than other areas (testing is usually the worst).
AAA/big studios want to try and train up a stable of really talented and loyal programmers, and want their guys for the long run. While some of the bigger indie studios can afford to the same, with most you'll find that you'll only be around for a project or two before you're booted out.
